How to Measure Squeezing and Entanglement of Gaussian States without Homodyning
06 Aug 2004-Physical Review Letters (American Institute of Physics)-Vol. 93, Iss: 6, pp 063601-063601
TL;DR: This work proposes a scheme for measuring the squeezing, purity, and entanglement of Gaussian states of light that does not require homodyne detection and needs only beam splitters and single-photon detectors.
Abstract: We propose a scheme for measuring the squeezing, purity, and entanglement of Gaussian states of light that does not require homodyne detection. The suggested setup needs only beam splitters and single-photon detectors. Two-mode entanglement can be detected from coincidences between photodetectors placed on the two beams.
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TL;DR: In this paper, the authors studied the generation and evolution of entangled light in a correlated spontaneous emission laser and derived the master equation for the two-mode field in a cavity and solved it analytically.
Abstract: We discuss the generation and evolution of entangled light in a correlated spontaneous emission laser. The master equation for the two-mode field in a cavity is derived and solved analytically. The time-dependent characteristic function in the Wigner representation for the two-mode field is obtained. It shows that the two-mode field in the cavity evolves in a two-mode Gaussian state. The entanglement degree of the two-mode field in the cavity increases initially, then decreases, and finally vanishes as the field evolves from an initial vacuum. The period of the entanglement is extended as the intensity of the driving field is increased. It is found that the entanglement still exists even when the two-mode squeezing disappears. During the entanglement period, the intensity of the field is amplified. The entanglement for the initial field being a two-mode squeezed vacuum and the entanglement of the output field are also discussed.
99 citations
Posted Content•
TL;DR: In this article, a review of hybrid approaches to optical quantum information processing is presented, in which both discrete and continuous degrees of freedom are exploited, with the aim of pushing the feasibility, the efficiencies, and the fidelities of linear schemes to the limits, potentially adding weak or measurement-induced nonlinearities to the toolbox.
Abstract: This article reviews recent hybrid approaches to optical quantum information processing, in which both discrete and continuous degrees of freedom are exploited. There are well-known limitations to optical single-photon-based qubit and multi-photon-based qumode implementations of quantum communication and quantum computation, when the toolbox is restricted to the most practical set of linear operations and resources such as linear optics and Gaussian operations and states. The recent hybrid approaches aim at pushing the feasibility, the efficiencies, and the fidelities of the linear schemes to the limits, potentially adding weak or measurement-induced nonlinearities to the toolbox.
79 citations
TL;DR: In this article, the correlation coefficient and the variance of the difference photocurrent for several classical and quantum states were measured and the results were in good agreement with theoretical predictions taking into account the extra noise in the generated fields that is due to the pump laser fluctuations.
Abstract: We address joint photodetection as a method for discriminating between the classical correlations of a thermal beam divided by a beam splitter and the quantum entanglement of a twin beam obtained by parametric down-conversion. We show that for intense beams of light the detection of the difference photocurrent may be used, in principle, in order to reveal entanglement, while the simple measurement of the correlation coefficient is not sufficient. We have experimentally measured the correlation coefficient and the variance of the difference photocurrent for several classical and quantum states. Results are in good agreement with theoretical predictions taking into account the extra noise in the generated fields that is due to the pump laser fluctuations.
62 citations
TL;DR: In this article, the decoherence of quantum states of continuous variable systems under the action of a quantum optical master equation resulting from the interaction with general Gaussian uncorrelated environments is quantified by relating it to the decay rates of various complementary measures of the quantum nature of a state, such as the purity, some nonclassicality indicators in phase space and, for two-mode states, entanglement measures and total correlations between the modes.
Abstract: We present a detailed report on the decoherence of quantum states of continuous variable systems under the action of a quantum optical master equation resulting from the interaction with general Gaussian uncorrelated environments. The rate of decoherence is quantified by relating it to the decay rates of various, complementary measures of the quantum nature of a state, such as the purity, some nonclassicality indicators in phase space and, for two-mode states, entanglement measures and total correlations between the modes. Different sets of physically relevant initial configurations are considered, including one- and two-mode Gaussian states, number states, and coherent superpositions. Our analysis shows that, generally, the use of initially squeezed configurations does not help to preserve the coherence of Gaussian states, whereas it can be effective in protecting coherent superpositions of both number states and Gaussian wave packets.
47 citations
TL;DR: In this article, the photon-added squeezed thermal state (PASTS), the excitation of displaced-squeezed chaotic field, and investigate its statistical properties, such as Mandel's Q-parameter, number distribution (as a Legendre polynomial), the Wigner function (WF).
42 citations
References
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TL;DR: A measure of entanglement that can be computed effectively for any mixed state of an arbitrary bipartite system is presented and it is shown that it does not increase under local manipulations of the system.
Abstract: We present a measure of entanglement that can be computed effectively for any mixed state of an arbitrary bipartite system. We show that it does not increase under local manipulations of the system, and use it to obtain a bound on the teleportation capacity and on the distillable entanglement of mixed states.
3,889 citations
TL;DR: In this article, the authors present the Deutsch-Jozsa algorithm for continuous variables, and a deterministic version of it is used for quantum information processing with continuous variables.
Abstract: Preface. About the Editors. Part I: Quantum Computing. 1. Quantum computing with qubits S.L. Braunstein, A.K. Pati. 2. Quantum computation over continuous variables S. Lloyd, S.L. Braunstein. 3. Error correction for continuous quantum variables S.L. Braunstein. 4. Deutsch-Jozsa algorithm for continuous variables A.K. Pati, S.L. Braunstein. 5. Hybrid quantum computing S. Lloyd. 6. Efficient classical simulation of continuous variable quantum information processes S.D. Bartlett, B.C. Sanders, S.L. Braunstein, K. Nemoto. Part II: Quantum Entanglement. 7. Introduction to entanglement-based protocols S.L. Braunstein, A.K. Pati. 8. Teleportation of continuous uantum variables S.L. Braunstein, H.J. Kimble. 9. Experimental realization of continuous variable teleportation A. Furusawa, H.J. Kimble. 10. Dense coding for continuous variables S.L. Braunstein, H.J. Kimble. 11. Multipartite Greenberger-Horne-Zeilinger paradoxes for continuous variables S. Massar, S. Pironio. 12. Multipartite entanglement for continuous variables P. van Loock, S.L. Braunstein. 13. Inseparability criterion for continuous variable systems Lu-Ming Duan, G. Giedke, J.I. Cirac, P. Zoller. 14. Separability criterion for Gaussian states R. Simon. 15. Distillability and entanglement purification for Gaussian states G. Giedke, Lu-Ming Duan, J.I. Cirac, P. Zoller. 16. Entanglement purification via entanglement swapping S. Parke, S. Bose, M.B. Plenio. 17. Bound entanglement for continuous variables is a rare phenomenon P. Horodecki, J.I. Cirac, M. Lewenstein. Part III: Continuous Variable Optical-Atomic Interfacing. 18. Atomic continuous variable processing and light-atoms quantum interface A. Kuzmich, E.S. Polzik. Part IV: Limits on Quantum Information and Cryptography. 19. Limitations on discrete quantum information and cryptography S.L. Braunstein, A.K. Pati. 20. Quantum cloning with continuous variables N.J. Cerf. 21. Quantum key distribution with continuous variables in optics T.C. Ralph. 22. Secure quantum key distribution using squeezed states D. Gottesman, J. Preskill. 23. Experimental demonstration of dense coding and quantum cryptography with continuous variables Kunchi Peng, Qing Pan, Jing Zhang, Changde Xie. 24. Quantum solitons in optical fibres: basic requisites for experimental quantum communication G. Leuchs, Ch. Silberhorn, E. Konig, P.K. Lam, A. Sizmann, N. Korolkova. Index.
2,940 citations
TL;DR: The Peres-Horodecki criterion of positivity under partial transpose is studied in the context of separability of bipartite continuous variable states and turns out to be a necessary and sufficient condition for separability.
Abstract: The Peres-Horodecki criterion of positivity under partial transpose is studied in the context of separability of bipartite continuous variable states. The partial transpose operation admits, in the continuous case, a geometric interpretation as mirror reflection in phase space. This recognition leads to uncertainty principles, stronger than the traditional ones, to be obeyed by all separable states. For all bipartite Gaussian states, the Peres-Horodecki criterion turns out to be a necessary and sufficient condition for separability.
1,796 citations
TL;DR: An inseparability criterion based on the total variance of a pair of Einstein-Podolsky-Rosen type operators is proposed for continuous variable systems and turns out to be a necessary and sufficient condition for inseparability.
Abstract: As with discrete systems, quantum entanglement also plays the basic role in quantum information protocols with continuous variables. A problem of great importance is then to check whether a continuous variable state, generally mixed, is entangled (inseparable). For discrete systems, there is the Peres-Horodecki inseparability criterion [1,2], based on the negativity of the partial transpose of the composite density operator. This negativity provides a necessary and sufficient condition for inseparability of 2 × 2 or 2 × 3 —dimensional systems. In this section, we will describe an entirely different inseparability criterion for continuous variable states, which was first proposed in Ref. [3]. The Peres-Horodecki criterion was also successfully extended to the continuous variable systems shortly afterwards, which will be described in the next section by Simon.
1,670 citations
Book•
13 Mar 1998
TL;DR: In this paper, the authors present a survey of classical models of light experiments with Photons, as well as non-demolition experiments with light and non-quantum noise.
Abstract: Classical Models of Light Experiments with Photons Quantum Models of Light Basic Optical Components Photo-currents: Generation and Detection The Laser Quantum Noise: Basic Measurements Sub-Poissonian Light Squeezing Experiments Quantum Non-demolition Experiments Applications of Quantum Optics Summary and Outlook Appendices Index.
817 citations